I know the Tigris and Euphrates rivers are in Iraq, but where do they start and end?Which way do they flow?

Answer 1

Euphrates

The headwaters of the Euphrates are the Murat and the Korasuyu (Karasu) in the Armenian Highland of Anatolia (Turkey). They join to form the Euphrates at Keban, near Elazig, forming a deep gorge. The river breaks through the Taurus Mountains and descends to the ancient kingdom of Commagenes. With the Mediterranean only 100 miles to the west at this reach, the Euphrates continues south and southeast into a relatively barren part of Syria, where the cultivable floodplain is no more than a few miles wide. Ample rainfall in the northern reaches of both these tributaries allowed the creation of major cities in ancient times.

From its confluence with the Al-Khabur down to Abu Kamal, the Euphrates flows through a broad agricultural region. Below the border with Iraq, the river once again narrows to an alluvial strip between limestone escarpments. Below Hit, the river begins to widen and irrigation increases.

Just south of the river below Ar-Ramadi lie Lakes Al-Habbaniyah and Al-Milh, both of which are large depressions. At Al-Hindiyah the river splits into two branches, Al-Hillah and Al-Hindiyah, each of which, over the centuries, alternately has assumed importance. Below An-Nasiriyah the river flows into marshes and then joins the Tigris at Al-Qurnah to form the Shatt al-'Arab.
Tigris

The Tigris, rising in a small mountain lake, Hazar Lake, southeast of Elazig, and fed by a number of small tributaries, drains a wide area of eastern Anatolia. After flowing beneath the impressive basalt walls of Diyarbakir, it receives the waters of the eastern Al-Khabur near the Syrian border at Cizre (Jazirhe-a-bin-Omar), entering Iraq a few miles beyond at Faysh Khabur.

The river ends in Iraq near An Nasireyah.

Answer 2

they flow East of South East into the Persian Gulf.

The river Euphrates is approximately 2,781 kilometers (1,730 miles) long. It is formed by the union of two branches, the Kara (the western Euphrates), which rises in the Armenian highlands of today's eastern Turkey north of Erzurum and the Murat (the eastern Euphrates), which issues from an area southwest of Mount Ararat, north of Lake Van. The upper reaches of the Euphrates flow through steep canyons and gorges, southeast across Syria, and through Iraq. The Khabur and the Balikh River join the Euphrates in eastern Syria.

Downstream, through its whole length, the Euphrates receives no further water flow. North of Basra, in southern Iraq, the river merges with the Tigris to form the Arvand/Shatt al-Arab, this in turn empties into the Persian Gulf.

The River Tigris is approximately 1,800 km (1,150 miles) long, rising in the Taurus Mountains of eastern Turkey and flowing in a generally southeasterly direction until it joins the Euphrates near Al Qurna in southern Iraq. Before it joins the Shatt al-Arab waterway, the river is joined by many tributaries, including the Diyala and both the Upper and Lower Zab rivers - all from the north.